z-Compact spaces

Abstract

Lindelof spaces, using multifunctions, are given.Our main results are .A space X is z-compact iff for every space Y and z-closed graph multifunction on X into Y the image of every z-closed set in X, is closed in Y. A space X is z-Lindelof iff for every P-space Y and z-closed graph multifunction on X into Y the image of every z-closed set in X is closed in Y.

Keywords

• compact spaces
• lindelof spaces compact space
• closed space
• pseudocompact space
• realcompact space